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For each model ensemble member, the ratio of σ from the historical run to σ from the observations was calculated, restricted to the shared period of 1982 2005 and an ensemble mean of this ratio was calculated for each model.
Further lambda values were calculated restricted to those GWAS results with P < 1E-2.
To examine possible nonlinear associations, we calculated restricted cubic splines for each study with more than three categories of exposure, using three fixed knots at 10%, 50%, and 90% through the total distribution of the reported intake, and combined them using multivariate meta-analysis 16, 17.
To examine possible nonlinear associations, we calculated restricted cubic splines for each study with more than three categories of exposure, using three fixed knots at 10, 50, and 90% through the total distribution of reported intake then combined using multivariate meta-analysis (19– 22).
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An expectation-maximization (EM) algorithm was proposed for calculating restricted maximum likelihood (REML) estimates of the residual and individual components of variances and covariances.
Finally, the incidence proportion calculated when restricted to using only child welfare reports (27.7%w; 95% CI: 23.0%w, 32.4%w) was nearly equivalent to the multi-source maltreatment report outcome (Fig. 3 ).
For sensitivity analysis, annual prevalence rates of pre-existing diabetes, GDM and all diabetes were calculated after restricting to women giving birth for the first time, and tests for linear trend were performed for this subgroup.
The electronic transitions between occupied and unoccupied states were calculated at Restricted Hartree Fock (RHF) and TDDFT/B3LYP level of theory using basis sets 6-31G and 6-31+G (d,p), with 100 singlet excited states that result in the UV absorption spectra and the main orbitals contributing to the transitions.
This is due to the fact that the number of calculated particles is restricted by the limit of computer memories.
The split plot error structure was then introduced into the reduced model by applying generalized least square equations with variance components calculated using the restricted maximum likelihood approach.
The HEF was calculated using a restricted matrix algorithm deconvolution technique [17].
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